Related papers: A Unified Approach to Discrepancy Minimization
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
Mirror Descent (MD) is a well-known method of solving non-smooth convex optimization problems. This paper analyzes the stochastic variant of MD with adaptive stepsizes. Its convergence on average is shown to be faster than with the fixed…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
In this paper, we construct an algorithm for minimising piecewise smooth functions for which derivative information is not available. The algorithm constructs a pair of quadratic functions, one on each side of the point with smallest known…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
We study discrete dynamics governed by a difference inclusion whose increment is the sum of a selection from a set-valued map and a noise term. For any bounded realization, convergence follows once the inter-iterate diameter is controlled…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…
It is a long-standing objective to ease the computation burden incurred by the decision making process. Identification of this mechanism's sensitivity to simplification has tremendous ramifications. Yet, algorithms for decision making under…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…